Observe that every coset
\(gG_v\) , \(v\in V\)  and \(g\in G\) ,
is an intersecting set, referred to as
a canonical intersecting set.
Clearly, in view of the above,
\(\rho (G)\ge 1\) . In particular,
for a transitive group \(G\)  it follows that
\(\rho (G)= 1\) 
if and only if
the maximum cardinality of an intersecting set is \(|G|/|V|\) .
Following [1]} we define \({\cal I}_n\)  to be the set
of all intersection densities of transitive permutation groups
of degree \(n\) :
\({\cal I}_n=\lbrace \rho (G) \colon G\textrm { transitive of degree } n\rbrace ,\) 
